## 23 Citations

### Degeneration of K3 surfaces with non-symplectic automorphisms

- Mathematics
- 2016

We prove that a K3 surface with an automorphism acting on the global $2$-forms by a primitive $m$-th root of unity, $m \neq 1,2,3,4,6$, does not degenerate (assuming the existence of the so-called…

### K3 surfaces with an order 60 automorphism and a characterization of supersingular K3 surfaces with Artin invariant 1

- Mathematics
- 2012

In characteristic $p=0$ or $p>5$, we show that a K3 surface with an order 60 automorphism is unique up to isomorphism. As a consequence, we characterize the supersingular K3 surface with Artin…

### Automorphisms of surfaces over fields of positive characteristic

- Mathematics
- 2021

We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and p-Jordan property. In particular, we show that the…

### Good reduction of K3 surfaces

- MathematicsCompositio Mathematica
- 2017

Let $K$ be the field of fractions of a local Henselian discrete valuation ring ${\mathcal{O}}_{K}$ of characteristic zero with perfect residue field $k$ . Assuming potential semi-stable reduction, we…

### A lifting of an automorphism of a K3 surface over odd characteristic

- Mathematics
- 2014

In this paper, we prove that, over an algebraically closed field of odd characteristic, a weakly tame automorphism of a K3 surface of finite height can be lifted over the ring of Witt vectors of the…

### CM liftings of $K3$ surfaces over finite fields and their applications to the Tate conjecture

- MathematicsForum of Mathematics, Sigma
- 2021

Abstract We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of $K3$ surfaces over finite fields. We prove that every $K3$…

### EPW sextics associated to K3 surfaces.

- Mathematics
- 2020

We give necessary and sufficient conditions for a $\langle 10 \rangle$-polarized Brill-Noether general K3 surface to be associated to a double EPW sextic which is a hyperkahler manifold. As a…

### ON THE FINITENESS OF TWISTS OF HYPERKÄHLER VARIETIES

- Mathematics
- 2021

Hyperkähler varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the finiteness of twists of hyperkähler varieties via a fixed finite field extension of characteristic…

### On the finiteness of twists of irreducible symplectic varieties

- Mathematics
- 2021

Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the finiteness of twists of irreducible symplectic varieties via a fixed finite field…

## References

SHOWING 1-10 OF 46 REFERENCES

### K3 surfaces with a symplectic automorphism of order 11

- Mathematics
- 2006

We classify possible finite groups of symplectic automorphisms of K3 surfaces of order divisible by 11. The characteristic of the ground field must be equal to 11. The complete list of such groups…

### Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic

- Mathematics
- 2004

We show that Mukai’s classication of nite groups which may act symplectically on a complex K3 surface extends to positive characteristic p under assumptions that (i) the order of the group is coprime…

### K3 surfaces with an order 60 automorphism and a characterization of supersingular K3 surfaces with Artin invariant 1

- Mathematics
- 2012

In characteristic $p=0$ or $p>5$, we show that a K3 surface with an order 60 automorphism is unique up to isomorphism. As a consequence, we characterize the supersingular K3 surface with Artin…

### On automorphisms of supersingular $K3$ surfaces

- Mathematics
- 1997

Let k be an algebraically closed field of positive characteristic which we take as the ground field. Let / : X —> C be a morphism from a nonsingular projective surface X to a nonsingular projective…

### The maximum order of finite groups of automorphisms of K3 surfaces

- Mathematics
- 1999

<abstract abstract-type="TeX"><p>Let <i>G</i> be a finite group of automorphisms of a <i>K</i>3 surface <i>X</i>. We shall show that |<i>G</i>| ≤ 3840 and if |<i>G</i>| = 3840, then the pair (<i>X,…

### Maximal subgroups of the Mathieu group $M_{23}$ and symplectic automorphisms of supersingular K3 surfaces

- Mathematics
- 2005

We show that the Mathieu groups $M_{22}$ and $M_{11}$ can act on the supersingular $K3$ surface with Artin invariant 1 in characteristic 11 as symplectic automorphisms. More generally we show that…

### Non-symplectic involutions of a K3 surface

- Mathematics
- 1995

We classify K3 surfaces with a non-symplectic finite automorphism of high order. It is shown that such an automorphism cannot be of order 60, and for each of the orders 38, 44, 48, 50, 54 and 66,…

### Intersection numbers of sections of elliptic surfaces

- Mathematics
- 1979

The theory of elliptic surfaces over C draws on ideas and techniques from arithmetic, geometry and analysis. Let f : X ~ S be a minimal elliptic fibration with non-constant j-invariant, which…

### Automorphisms of Jacobian Kummer surfaces

- MathematicsCompositio Mathematica
- 1997

We study automorphisms of a generic Jacobian Kummer surface. First weanalyse the action of classically known automorphisms on the Picard lattice of the surface, then proceed to construct new…